Multi-Decadal to Centennial Oscillations and Climate Signals Inferred
by Periodic Solar Forcing
Mao-Chang Liang1,2,3*, et al.
1
Research Center for Environmental Changes, Academia Sinica, Taiwan
2
Graduate Institute of Astronomy, National Central University, Taiwan
3
*
Institute of Astronomy and Astrophysics, Academia Sinica, Taiwan
To whom correspondence should be addressed: mcl@rcec.sinica.edu.tw
Abstract
Climate sensitivity is a measure of the response of the climate system to the
changes of external forcings such as anthropogenic greenhouse emissions and solar
radiation (ref. IPCC). General circulation models provide a means to
quantitatively resolve the interaction (refs). Here we show that the oceanic mixed
layer depth plays an important role in modifying the multi-decadal to centennial
oscillations of the sea surface temperature, which in turn affect the derived climate
sensitivity at various phases of the oscillations. The eleven-year periodic solar
forcing is used to measure the sensitivity. The derived amplitude of the response
varies from nearly 0 to ~0.1 K per 1 Wm-2 change of solar constant, with the upper
limit close to that derived observationally (Tung, Zhou, Camp GRL 2008); the
underlying envelop oscillates at ~200-300 years.
The oceans are the largest heat reservoir on the planet. The top ~100 meter layer defines
the mixed layer where energy/heat is well mixed and the temperature gradient is small.
The depth of the layer controls the amount and efficiency of heat going to the ocean; the
deeper the mixed layer the less variable the climate system is.
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more on introduction/motivation and ocean/heat transport
The study is conducted using the released version of GISS-HYCOM (GISSEH)
atmosphere-ocean coupled climate model (Sun and Bleck Clim. Dyn. 2006). To isolate
the response due to solar forcing, anthropogenic (greenhouse gases and aerosols) and
volcanic emissions are not considered; the amount of greenhouse gases and atmospheric
aerosol loading is kept at pre-industrial level. A pure sinusoidal solar forcing is imposed
at a period of eleven years with peak-to-peak amplitude of 0.1% for total insolation and
2% for solar flux at wavelengths less than 295 nm. Ozone concentration varies
accordingly with the flux of dissociative UV photons (Shindell et al. GRL 2006); no
anthropogenic source is included. The standard model uses the default setup. Sensitivity
of the model results to the changes of oceanic mixed layer depth is also presented, as
the depth plays a critical role in controlling the heat flux between the atmosphere and
the underlying ocean, which in turn modifies the degree of the response to the changes
of solar radiation (and anthropogenic forcings).
In the present models, solar radiation is the only perturbed parameter. To study the
response,  defined by
 = T/S,
where T is the change of temperature to the change of solar constant S (Tung, Zhou,
Camp GRL 2008). Statistical methods like composite mean difference (CMD) (Camp
and Tung 2007) and linear discriminant analysis (LDA) (Schneider and Held, 2001;
Tung and Camp, 2008) are used to retrieve solar signals. a few more words on the two
methods; the advantage of the methods
Applying LDA to the standard model monthly data shows a remarkable correlation
between the deduced global temperature response and the solar radiation variability
(Figure 1). The correlation coefficient,  = xx, is highly statistically significant. A
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bootstrap Monte-Carlo test with replacement shows that a single optimal filter exists
that separates the temperature in solar max from that in solar min and that the large
observed separability measure R could not be obtained by chance at over xx%
confidence level. The measure  gives a value of xxxxx K/Wm-2 at phase lag 0; the
error bar defines a 2- standard deviation (95% confidence level). The value is
somewhat lower than the observed by a factor 2-3. Slightly larger value of  at phase
lag 1 year, a value that is close to that determined observational (Tung et al.), suggests
that the model is close to being in steady state. Such underestimation could be largely
reduced by a less efficient ocean mixing model. reduced ocean mixing model …
The spatial pattern associated with the derived time series is shown in Figure 2. more on
the results
The consecutive  values derived for 100-year duration is shown in Figure 3.
The heat flux between the atmosphere and the underlying ocean is shown in Figure 4.
Implication/discussion
References:
Acknowledgements
This work was supported in part by NSC grant 98-2111-M-001-014-MY3 to Academia
Sinica.
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Figure 1: (a)100 year dT and dS vs. time. (b) variance ratio. (c) kappa value as a
function of lag two curves: standard model and reduced ocean mixing model (select
high kappa period)
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Figure 2: the corresponding spatial patterns associated with the above kappa values at
lag 0
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Figure 3: kappa value as a function of time; kappa was obtained for every 100 year
duration
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Figure 4: heat flux to the ocean for standard model and reduced ocean mixing model at
maximum kappa value. Also 100 years averaged
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